This is a love song of the "I can't believe how lucky I am that an angel like you is with a mess like me" variety.
In the first verse, the speaker explains he is a mess because he is frantic with a "fever"-ish panic, and she douses that with "cool water." In case that isn't clear, he repeats that he was "in a crazy motion" and that she "calmed [him] down."
In the second verse, the speaker is a mess because he is emotionally closed off. While the speaker of "I Am a Rock" says: "I build walls deep and mighty/ That none may penetrate," that seems small next to the wall this speaker builds, which is "a thousand miles long" (the Great Wall of China is about 4,000 miles long, incidentally). Yet, she was able overcome these formidable defenses and "to get next to" him.
In the bridge, he talks about how "some people" can't bring themselves to say "I love you," let "long" to "be told" exactly that. Hmmm, who might one of those hypothetical "people" be? This is yet another way he is a mess.
The chorus adds a fourth: "When something goes wrong/ I'm the first to admit it." This certainly means he is willing to admit that something is awry or amiss. But while it doesn't say he also accepts responsibility for the problem, it sort of implies that he does.
Meanwhile, "When something goes right," he is so pessimistic that he he can't believe or accept that it did happen: "It's apt to confuse me/It's such an unusual sight."
He is so used to things going wrong, he "can't get used to something so right." He is so accustomed to disappointment that he can't acknowledge that something good has happened to him, and he can't trust that it will last.
So here we have an anxious, introverted, undemonstrative person with a tendency toward doubt... and self-doubt. No one can say this person is not self-aware-- even a bit self-critical.
Yet, this amazing woman felt he was still worth it, and stuck with him until he was able to trust and appreciate her. With this song, he thanks her and expresses his astonishment that she is with him at all, let alone still with him.
This song is the inverse of a song like "My Funny Valentine," in which the woman says what's wrong with the man, yet she still loves him. This might be his response, in which he says, "Me? You want me? My mouth is a little weak and my figure is less than Greek! You... sure? Wow! That's great!"
Musical note: A previous incarnation of this song is called "Let Me Live in Your City." The verses are the same, but the choruses, which have the same melody of the final version, have these lyrics:
"Let me live in your city
The river’s so pretty, the air is so fine
Let me room where I can lay over
I’m just a traveler eating up travelin’ time
I’m just a traveler eating up
My travelin’ time."
IMPACT: The song went to #7 on the UK charts. It is very popular among female singers. British songstress Annie Lennox covered it on her Medusa album. It was also covered by Barbra Streisand, Simon collaborator Phoebe Snow, and country singer Trisha Yearwood. Someone tell Adele.
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